What it does
When two drugs are given together, the combined effect can be more than expected (synergy), about as expected (additivity) or less (antagonism). “Expected” needs a reference model, and the field uses several. This page takes a checkerboard experiment (a dose matrix of two drugs, each well’s response as % inhibition) and compares every combination well with three reference models, draws the differences as a heatmap and gives summary scores.
It is for study and teaching, not medical advice. It analyses data from an experiment; it does not suggest doses.
How to use it
- Paste the matrix. The first row holds drug B’s doses after a corner cell; each following row starts with a drug A dose, then the responses at each drug B dose. Both drugs need a dose of 0, so the matrix includes each drug alone. Up to 20 × 20 wells. Or use Open a file.
- Responses must be % inhibition: 0 means no effect and 100 a full effect. If you measured viability, use 100 − % viability.
- Name the drugs and their units for the labels.
- Choose the top of the single-drug curves. Fixed at 100 % is the median-effect model of Chou and Talalay. Fitted lets each drug level off lower; if a curve does not level off within your doses, the top is set back to 100 % and the page says so.
- Pick the heatmap: excess over Bliss, HSA or Loewe, the combination index (CI), or the observed matrix.
The models
- Bliss independence: the drugs act independently, so the expected inhibition is EA + EB − EA·EB, using the measured single-drug wells.
- Highest single agent (HSA): the combination should beat the better of the two drugs alone at those doses.
- Loewe additivity: each drug behaves like a dilution of the other. The expected effect E solves a / DxA(E) + b / DxB(E) = 1, where DxA and DxB come from Hill curves fitted to each drug alone: E = top × dʰ / (EC50ʰ + dʰ).
- Combination index: CI = a / DxA + b / DxB at the observed effect. Below 1 is synergy, 1 additivity, above 1 antagonism. It is not defined when the observed effect is beyond a curve’s top.
The excess of a well is observed − expected in % points. Scores are averaged over the combination wells (both doses above 0); the CI summary is a geometric mean.
Worked example
The example is a made-up 6 × 6 matrix. With the top fixed at 100 %, drug A’s curve has an EC50 of 0.8164 µM (Hill slope 1.20) and drug B’s 13.34 nM (slope 0.884). The page shows a mean excess over Bliss of +2.31 (highest +6.23 at 0.3 µM and 1 nM), a mean HSA excess of +9.20, a mean Loewe excess of +5.28 and a combination index of 0.643, with 22 of the 24 wells below 0.9. In the well at 0.3 µM and 3 nM the observed inhibition is 43.8 %, Bliss expects 39.5 % and Loewe 36.6 %, and the CI is 0.75. So the drugs look mildly synergistic by Loewe and CI, and close to additive by Bliss.
Tips
- The models answer different questions and often disagree, as here. Report which one you used.
- Use replicate plates and average them before pasting; a single noisy well can make a strong-looking spot.
- Doses should bracket each drug’s EC50 so the single-drug curves are well defined.
FAQ
Is ZIP included? Not yet; Bliss, HSA, Loewe and CI are.
Why are the single-drug wells 0 on the Bliss map? Bliss uses them as its reference, so they match by definition.
Is my data uploaded? No. Everything runs in this page.
Where the numbers come from
- Bliss independence: C. I. Bliss, Ann. Appl. Biol. 26 (1939) 585. Loewe additivity: S. Loewe and H. Muischnek, Arch. Exp. Pathol. Pharmakol. 114 (1926) 313. Combination index: T.-C. Chou and P. Talalay, Adv. Enzyme Regul. 22 (1984) 27; M. C. Berenbaum, Pharmacol. Rev. 41 (1989) 93. Single-drug wells for Bliss and HSA as in SynergyFinder: A. Ianevski et al., Bioinformatics 33 (2017) 2413. Formulas only; no data or tables copied.
- Calculations written by fibub. Checked in the tests against an independent Python implementation (SciPy curve_fit Hill fits with several starts, brentq for the Loewe surface) on the example and 20 random matrices: Hill parameters agree to 3 × 10⁻⁵, every well to 3 × 10⁻⁴ % points; also against sham combinations (a drug with itself gives CI = 1).
- The example matrix is made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.